• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.843-850
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• 2002

Linear transformation theory has been effectively used in the design and analysis of prestressed concrete structures. The underlying assumptions of the theory, which were often overlooked, are investigated in the respect of equivalent load method. As a result, it is found that the same equivalent loading system is produced for all the cases of the linear transformation by the assumptions of the conventional equivalent load method. On the other hand, equivalent loading systems in a strict and accurate sense do not satisfy the classical theories of the linear transformation. Also, it is shown that a little different equivalent loading system from the conventional one is obtained for each linear transformation according to the proposed equivalent load method that is derived from the self-equilibrium property of the tendon-induced forces. Therefore, it can be concluded that the linear transformation theory is valid only when referring to the conventional approximate equivalent load method. The discussions are further extended to the eccentrically located circumferential tendon in the wall of containment structures, where the problem of eccentricity is analyzed also from the view point of the linear transformation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.1 s.244
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• pp.66-75
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• 2006

Nonlinear response structural optimization using equivalent static loads (NROESL) has been proposed. Nonlinear response optimization is solved by sequential linear response optimization with equivalent static loads which are generated from the nonlinear responses and linear stiffness matrix. The linear stiffness matrix should be obtained in NROESL, and this process can be fairly difficult for some applications. Proportional transformation of loads (PTL) is proposed to overcome the difficulties. Equivalent static loads are obtained by PTL. It is the same as NROESL except for the process of calculating equivalent static loads. PTL is developed for large-scale probems. First, linear and nonlinear responses are evaluated from linear and nonlinear analyses, respectively. At a DOF of the finite element method, the ratio of the two responses is calculated and an equivalent static load is made by multiplying the ratio and the loads for linear analysis. Therefore, the mumber of the equivalent static loads is as many as that of DOF's and an equivalent static load is used with the reponse for the corresponding DOF in the optimization process. All the equivalent static loads are used as multiple loading conditions during linear response optimization. The process iterates until it converges. Examples are solved by using the proposed method and the results are compared with conventional methods.

• Journal of the Korean Geotechnical Society
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• v.25 no.8
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• pp.57-64
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• 2009

In this study, a method using equivalent transformation for estimation of the axial load capacity of tapered piles is proposed. While preexistent methods for estimating the axial load capacity of tapered piles have been based on the effect of soil state and taper angle, a new design method is proposed considering cone resistance $q_c$ and equivalent transformation in sand. Through tapered pile simplified by using equivalent transformation, a new method fur quick and easy estimation of the axial load capacity of tapered pile is proposed for practical use. In order to verify the proposed method, calibration chamber test and field test were conducted. In calibration chamber test, comparison of estimated axial load capacity with measured one showed that the standard deviation and COV (Coefficient Of Variation) of estimated $Q_t$ is $0.05{\sim}0.121$, $0.04{\sim}0.05$ respectively. For field test, axial load capacity by proposed method shows 2.5% under-estimation in comparison with measured value. As a result, it is found that proposed method produces satisfactory predictions for tapered piles.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.5
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• pp.419-425
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• 2007

A rapid one-shot alignment method of the Strapdown INS (SDINS) for a vertical launch is proposed. The proposed alignment is performed using the accelerometer output of the Slave INS and the attitude of the Master INS. To improve the accuracy and the speed of the alignment, the equivalent linear transformation and the pre-filtering method are developed. Experiment results show that the proposed method is effective in improving the accuracy and the speed of the alignment.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.4
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• pp.458-467
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• 2012

In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.

• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.383-392
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• 2009

The static and dynamic analyses of simply supported beams are studied by using the U-transformation method and the finite difference method. When the beam is divided into the mesh of equal elements, the mesh may be treated as a periodic structure. After an equivalent cyclic periodic system is established, the difference governing equation for such an equivalent system can be uncoupled by applying the U-transformation. Therefore, a set of single-degree-of-freedom equations is formed. These equations can be used to obtain exact analytical solutions of the deflections, bending moments, buckling loads, natural frequencies and dynamic responses of the beam subjected to particular loads or excitations. When the number of elements approaches to infinity, the exact error expression and the exact convergence rates of the difference solutions are obtained. These exact results cannot be easily derived if other methods are used instead.

• Proceedings of the KIEE Conference
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• 1988.11a
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• pp.388-393
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• 1988

New circuit D-Q transformation concept is introduced to analyze AC converters such as inverters, rectifiers and cyclo-converters with ease. The equivalent linear time invariant circuit is obtained by substituting switches with equivalent turn-ratio variable transformers and changing balanced AC reactors into equivalent DC reactors combined by gyrators. This circuit enables us to utilize the powerful linear system analysis techniques such as Laplace transform otherwise which could not be applied to the time varying switching systems. Direct substitution of switches of DC converters with transformers is shown as a preliminary. Then the modeling procedure is shown for a controlled rectifier-inverter circuit. Finally an analysis example is proposed for a buck-boost inverter and the result is compared with the conventional approach. This approach is applicable to all AC converter families to determine the AC transfer functions and the DC operating points. It is identified that the switching systems are equivalent to the RLC filter circuits with transformers and gyrators.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1845-1847
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• 1991

In general, it is not easy to find the linearizing coordinate transformation map for a class of systems which are state equivalent to linear systems, because it is required to solve a set of partial differential equations. It is possible to construct an arbitrary nonlinear function with a backpropagation(BP) net. Utilizing this property of BP neural net, we construct a desired linearizing coordinate transformation map. That is, we implement a unknown coordinate transformation map through the training of neural weights. We have shown an example which supports this idea.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1401-1409
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• 2016

In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.401-410
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• 2008

The natural frequency of a beam plays an important role in not only vibration analysis but also understanding its dynamic characteristics. It is complicated to analyse the natural frequency of a stepped beam with discontinuously varying section. Approximate analysis methods such as Rayleigh-Ritz method, FEM, etc. are frequently used for the vibration analysis of stepped beams. In such a case, accuracy of these methods depends upon the number of partitioned elements, the number of the iterations in calculation and the assumed mode shape. This study presents an approximate analysis method for the fundamental natural frequency analysis of stepped cantilever beam, using equivalent beam transformation technique. Validity and usefulness are verified by comparing the proposed method with FEM for several example problems.